How to naturally connect objects of different shapes
Here is a way using Grid Fill.

UPDATE: check out the "Bridge Edge Loop" option proposed by @RayMairlot in the comments. It may be best suited to your need.

ref: https://docs.blender.org/manual/en/latest/modeling/meshes/editing/faces.html#grid-fill


Subdivide the side to match the number of vertices on the other side
Create supporting Edges
Select edges on both sides
Grid fill
repeat for the other sides.